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    <title>equil</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>equil</b> -  balancing of pair of symmetric matrices</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>T=equil(P,Q)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>P, Q</b>
        </tt>: two positive definite symmetric matrices</li>
      <li>
        <tt>
          <b>T</b>
        </tt>: nonsingular matrix</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
      <tt>
        <b>equil</b>
      </tt> returns <tt>
        <b>t</b>
      </tt> such that:</p>
    <p>
      <tt>
        <b>T*P*T'</b>
      </tt> and  <tt>
        <b>inv(T)'*Q*inv(T)</b>
      </tt>  are both equal to a same 
    diagonal and positive matrix.</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

P=rand(4,4);P=P*P';
Q=rand(4,4);Q=Q*Q';
T=equil(P,Q)
clean(T*P*T')
clean(inv(T)'*Q*inv(T))
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="equil1.htm">
        <tt>
          <b>equil1</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../linear/balanc.htm">
        <tt>
          <b>balanc</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="ctr_gram.htm">
        <tt>
          <b>ctr_gram</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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